Research Interests

Revealing Quantum Flow
This is my most current research project, and it has received some very positive
attention. Here's the text of the official press release from U. Hertfordshire (slightly adapted):

There are no phase space trajectories in quantum physics but that is
not the full story. Together with my UK-based colleagues, Dimitris
Kakofengitis and Georg Ritter, we have found that a new powerful tool one can
call `Wigner flow' is the quantum analog of phase space flow. Wigner
flow provides information for quantum dynamics similar to that gleaned
from phase space trajectories in classical physics. Wigner flow can be
used for the visualisation of quantum dynamics. Additionally, and
perhaps even more importantly, Wigner flow helps with the abstract
analysis of quantum dynamics using topological methods.

Understanding a dynamical system can be very hard, in the case of
`chaotic' systems prohibitively so. Scientists have therefore
developed an arsenal of visualisation tools to glimpse structures
which would otherwise be missed. Physicists like to plot systems'
dynamics in an arena they call `phase space'. Essentially, phase space
uses coordinates suitable for the study of a system's dynamics. Phase
space methods have found applications in fields spanning mechanics,
electrical engineering, and population dynamics in ecology.

In phase space, trajectories generated by the systems' dynamics --be
they measured, or generated through computer code-- are plotted.
Widely known examples are `strange attractors' of chaotic systems such
as the well known Lorenz attractor. They illustrate well the power of
phase space methods; although there had been hints of the existence of
chaotic systems since the late 19th century it was only with modern
computers that chaos in dynamical systems became recognized and its
study accessible.

In classical physics phase space trajectories give rise to flow-fields
representing the dynamics of the system along its trajectories; they
yield additional insight into a system's behaviour.

Quantum theory phase space trajectories do not exist because
Heisenberg's uncertainty principle does not allow for the formation of
sharply defined trajectories. But quantum physicists have not given up
entirely on phase space. The study of the next best thing, the
movement of quantum physics' phase space-based probability
distributions has actually boomed in recent years.

Sophisticated schemes for the reconstruction of the most prominent of
these distributions, `Wigner's function', from experimental data, have
set quantum phase space analysis on a firm footing. Yet, since quantum
trajectory studies cannot be carried out, some of the power of
established classical methods is missing.

Because trajectories are missing in quantum phase space, physicists
did not pay much attention to the associated flow-fields, although
these do exist. Our `Physical Review Letters' paper, coming out in December 2012,
we show that quantum phase space flow is well worth studying.
We have been studying Wigner flow, which is based on the dynamics
of Wigner's function, and shown that it reveals new and surprising
features of quantum phase space dynamics. It forms, for example,
vortices that spin the `wrong' way round and which appear in the
`wrong' part of phase space, when viewed from a classical physics
standpoint. So, such dynamical patterns are manifestations of the
quantum nature of the system.

On top of such new riches our team has established the existence of a
conservation law that reveals a new type of topological order for
quantum dynamics. As an application we have shown that Wigner flow
sheds new light on quantum tunnelling, the fundamental process that
governs the workings of electronic computer circuits, and also the
decay of radio-nuclides.

For further information, see the
animations
that illustrate Wigner flow.

Helices of light
Earlier in 2012 I published a nice piece of work on laser beams that can be made to form dark as well as
bright intensity helices, or corkscrews of light.
They can arise as an interference phenomenon. It turns out that threads of darkness, dark helices, fare better than bright ones. They are less constrained by optical resolution limits.
Dark helices are much more sharply defined than bright helices when you "see" them on a logarithmic scale, photo-resists tend to do just that. They are potentially more useful in laser tweezing arrangements since they are dark. This means less light is scattered when you trap a low field seeking particle. That may turn out be important for applications such as atom-trapping, trapping of molecules with handedness in solution, or bulk production of helical photo-lithographic imprints; to create metamaterials, say.
Here are a couple of links that explain it quite well.